Using Persistent Homology to Represent Online Social Network Graphs

Abstract

Online Social Networks (OSNs) are simple, unweighted graphs used to store information in the context of social media and emails. Accurately representing the connectivity and features of these graphs is important in applications of graph utility and differential privacy. Current methods of describing these network graphs use graph metrics such as the shortest-path betweenness centrality, clustering coefficient, and degree distribution. Although these metrics are sufficient in providing information about a particular aspect of network graphs, they fail to give a multi-faceted snapshot of an OSN. Persistent homology provides a novel method for a comprehensive visual representation of the information stored in network graphs. By translating a network graph to a persistent homology barcode format, the correlation in key features between the figures will be observed against various utility metrics. This paper evaluates the persistent homology barcodes of OSNs across social media platforms and provides a means of analyzing network graphs without revealing sensitive information.